Section 3107F — California Building Code (Title 24, Part 2)

STRUCTURAL ANALYSIS AND

DESIGN OF COMPONENTS

3107F.1 General.¶

3107F.1.1 Purpose. This section establishes the minimum performance standards for structural and nonstructural components. Evaluation procedures for seismic perfor- mance, strength and deformation characteristics of con- crete, steel and timber components are prescribed herein. Analytical procedures for seismic assessment are pre- sented in Section 3104F.

3107F.1.2 Applicability. This section addresses MOT structures constructed using the following structural com- ponents:

1. Reinforced concrete decks supported by batter and/ or vertical concrete piles

2. Reinforced concrete decks supported by batter and/ or vertical steel piles, including pipe piles filled with concrete

3. Reinforced concrete decks supported by batter and/ or vertical timber piles

4. Timber decks supported by batter or vertical timber, concrete or steel pipe piles

5. Retaining structures constructed of steel, concrete sheet piles or reinforced concrete

Additionally, this section addresses structural and non- structural components, nonbuilding structures and build- ing structures comprised of steel, concrete or timber.

3107F.2 Concrete deck with concrete or steel piles.¶

3107F.2.1 Component strength. The following parame- ters shall be established in order to compute the compo- nent strength:

1. Specified concrete compressive strengths

2. Concrete and steel modulus of elasticity

3. Yield and tensile strength of mild reinforcing and prestressed steel and corresponding strains 4. Confinement steel strength and corresponding strains

5. Embedment length

6. Concrete cover

7. Yield and tensile strength of structural steel

8. Ductility

In addition, for “existing” components, the following conditions shall be considered:

9. Environmental effects, such as reinforcing steel cor- rosion, concrete spalling, cracking and chemical attack

10. Fire damage

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11. Past and current loading effects, including over- load, fatigue or fracture

12. Earthquake damage

13. Discontinuous components

14. Construction deficiencies

3107F.2.1.1 Material properties. Material properties of existing components, not determined from testing procedures, and of new components, shall be estab- lished using the following methodology.

The strength of structural components shall be eval- uated based on the following values (Section 5.3 of

[7.1] and pp. 3-73 and 3-74 of [7.2]):

Specified material strength shall be used for non- ductile components (shear controlled), all mechanical, electrical and mooring equipment (attachments to the deck) and for all non seismic load combinations:

f ′ c = 1.0 f ′ c (7-1a) fy = 1.0 fy (7-1b) fp = 1.0 fp (7-1c)

In addition, these values (7-1a, 7-1b and 7-1c) may be used conservatively as alternatives to determine the nominal strength of ductile components (N).

Expected lower bound estimates of material strength shall be used for determination of moment- curvature relations and nominal strength of all ductile components:

f ′ c = 1.3 f ′ c (7-2a) fy = 1.1 fy (7-2b) fp = 1.0 fp (7-2c)

Upper bound estimates of material strength shall be used for the determination of moment-curvature rela- tions, to obtain the feasible maximum demand on capacity protected members:

f ′ c = 1.7 f ′ c (7-3a) fy = 1.3 fy (7-3b) fp = 1.1 fp (7-3c)

where:

f ′ c =Specified compressive strength of concrete

fy = Specified yield strength of reinforcement or

specified minimum yield stress steel

fp = Specified yield strength of prestress strands

“Capacity Design” (Section 5.3 of [7.1]) ensures that the strength at protected components (such as pile caps and decks), joints and actions (such as shear), is greater than the maximum feasible demand (over strength), based on realistic upper bound estimates of plastic hinge flexural strength. An additional series of nonlinear analyses using moment curvature character- istics of pile hinges may be required.

5.3 of [7.1]) ensures_ that the strength at protected components (such as pile caps and decks), joints and actions (such as shear), is greater than the maximum feasible demand (over strength), based on realistic upper bound estimates of plastic hinge flexural strength. An additional series of nonlinear analyses using moment curvature character- istics of pile hinges may be required.

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Alternatively, if a moment-curvature analysis is per- formed that takes into account the strain hardening of the steel, the demands used to evaluate the capacity protected components may be estimated by multiplying the moment-curvature values by 1.25.

Based on a historical review of the building materi- als used in the twentieth century, guidelines for tensile and yield properties of concrete reinforcing bars and the compressive strength of structural concrete have been established (see Tables 10-2 to 10-4 of ASCE/SEI 41 [7.3]). The values shown in these tables can be used as default properties, only if as-built information is not available and testing is not performed. The values in Tables 31F-7-1 and 31F-7-2, are adjusted according to Equations (7-1) through (7-3).

3107F.2.1.2 Knowledge factor (k). Knowledge factor, k, shall be applied on a component basis.

The following information is required, at a mini- mum, for a component strength assessment:

1. Original construction records, including draw- ings and specifications.

2. A set of “as-built” drawings and/or sketches, documenting both gravity and lateral systems (Section 3102F.1.5) and any postconstruction modification data.

3. A visual condition survey, for structural compo- nents including identification of the size, location and connections of these components.

TABLE 31F-7-1 COMPRESSIVE STRENGTH OF STRUCTURAL CONCRETE (psi) ¹

TIME FRAME	PILING	BEAMS	SLABS
1900-1919	2,500-3,000	2,000-3,000	1,500-3,000
1920-1949	3,000-4,000	2,000-3,000	2,000-3,000
1950-1965	4,000-5,000	3,000-4,000	3,000-4,000
1966-present	5,000-6,000	3,000-5,000	3,000-5,000

1. Concrete strengths are likely to be highly variable for an older structure.

TABLE 31F-7-2 TENSILE AND YIELD PROPERTIES OF REINFORCING BARS FOR VARIOUS ASTM SPECIFICATIONS AND PERIODS

(after Table 6-2 of [7.3])

ASTM	STEEL TYPE	YEAR RANGE3	GRADE	STRUCTURAL1	INTERMEDIATE1	HARD1
*ASTM*	*STEEL* *TYPE*	*YEAR RANGE3*	*GRADE*	33	40	50	60	70	75
*ASTM*	*STEEL* *TYPE*	*YEAR RANGE3*	*Minimum Yield2 (psi)*	*33,000*	*40,000*	*50,000*	*60,000*	*70,000*	*75,000*
*ASTM*	*STEEL* *TYPE*	*YEAR RANGE3*	*Minimum Tensile2 (psi)*	*55,000*	*70,000*	*80,000*	*90,000*	*95,000*	*100,000*
A15	Billet	1911-1966		X	X	X
A16	Rail4	1913-1966				X
A61	Rail4	1963-1966					X
A160	Axle	1936-1964		X	X	X
A160	Axle	1965-1966		X	X	X	X
A408	Billet	1957-1966		X	X	X
A431	Billet	1959-1966							X
A432	Billet	1959-1966					X
A615	Billet	1968-1972			X		X		X
A615	Billet	1974-1986			X		X
A615	Billet	1987-1997			X		X		X
A616	Rail4	1968-1997					X
A617	Axle	1968-1997			X		X
A706	Low-Alloy5	1974-1997						X
A955	Stainless	1996-1997			X		X		X

General Note: An entry “X” indicates that grade was available in those years. 1. The terms structural, intermediate and hard became obsolete in 1968. 2. Actual yield and tensile strengths may exceed minimum values. 3. Until about 1920, a variety of proprietary reinforcing steels were used. Yield strengths are likely to be in the range from 33,000 psi to 55,000 psi, but higher values are possible. Plain and twisted square bars were sometimes used between 1900 and 1949. 4. Rail bars should be marked with the letter “R.” 5. ASTM steel is marked with the letter “W.”

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4. In the absence of material properties, values from limited in-situ testing or conservative estimates of material properties (Tables 31F-7-1 and 31F-7-2).

5. Assessment of component conditions, from an in- situ evaluation, including any observable deteri- oration.

6. Detailed geotechnical information, based on recent test data, including risk of liquefaction, lateral spreading and slope stability.

The knowledge factor, k, is 1.0 when comprehensive knowledge as specified above is utilized. Otherwise, the knowledge factor shall be 0.75 (see Section 5.2.6 of ASCE/SEI 41 [7.3]). 3107F.2.2 Component stiffness. Stiffness that takes into account the stress and deformation levels experienced by the component shall be used. Nonlinear load-deformation relations shall be used to represent the component load- deformation response. However, in lieu of using nonlinear methods to establish the stiffness and moment curvature relation of structural components, the equations of Table 31F-7-3 may be used to approximate the effective elastic stiffness, EIe, for lateral analyses (see Section 3107F.8 for definition of symbols).

TABLE 31F-7-3 EFFECTIVE ELASTIC STIFFNESS

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relation. The displacement demand and capacity shall be calculated per Sections 3104F.2 and 3104F.3, as appro- priate.

The moment-rotation relationship for concrete compo- nents shall be derived from the moment-curvature analysis per Section 3107F.2.5.4 and shall be used to determine lateral displacement limitations of the design. Connection details shall be examined per Section 3107F.2.7.

3107F.2.4 Stress-Strain models.

3107F.2.4.1 Concrete. The stress-strain model and terms for confined and unconfined concrete are shown in Figure 31F-7-1.

3107F.2.4.2 Reinforcement steel and structural steel. The stress-strain model and terms for reinforcing and structural steel are shown in Figure 31F-7-2.

3107F.2.4.3 Prestressed steel. The stress-strain model of Blakeley and Park [7.4] may be used for prestressed steel. The model and terms are illustrated in Figure 31F-7-3.

3107F.2.4.4 Alternative stress-strain models. Alterna- tive stress-strain models are acceptable if adequately documented and supported by test results, subject to Division approval.

FIGURE 31F-7-1 STRESS-STRAIN CURVES FOR CONFINED

AND UNCONFINED CONCRETE [7.1]

FIGURE 31F-7-2 STRESS-STRAIN CURVE FOR MILD REINFORCING

STEEL OR STRUCTURAL STEEL [7.1]

CONCRETE COMPONENT	EI /EI e g
Reinforced Pile	0.3 + N/(f 'c Ag)
Pile/Deck Dowel Connection1	0.3 + N/(f 'c Ag)
Prestressed Pile1	0.6 < EIe /EIg < 0.75
Steel Pile	1.0
Concrete w/ Steel Casing	Es Is 0.25_ Ec Ic_ + Es Is Ec Ic + ( ) ---------------------------------------
Deck	0.5

1. The pile/deck connection and prestressed pile may also be approximated as one member with an average stiffness of 0.42 EIe /EIg (Ferritto et al, 1999 [7.2]) N = is the axial load level. Es = Young‘s modulus for steel Is = Moment of inertia for steel section Ec = Young‘s modulus for concrete Ic = Moment of inertia for uncracked concrete section 3107F.2.3 Deformation capacity of flexural members. Stress-strain models for confined and unconfined con- crete, mild and prestressed steel presented in Section 3107F.2.4 shall be used to perform the moment-curvature analysis.

s modulus for steel_ Is = Moment of inertia for steel section Ec = Young‘s modulus for concrete Ic = Moment of inertia for uncracked concrete section 3107F.2.3 Deformation capacity of flexural members. Stress-strain models for confined and unconfined con- crete, mild and prestressed steel presented in Section 3107F.2.4 shall be used to perform the moment-curvature analysis.

The stress-strain characteristics of steel piles shall be based on the actual steel properties. If as-built informa- tion is not available, the stress-strain relationship may be obtained per Section 3107F.2.4.2.

For concrete in-filled steel piles, the stress-strain model for confined concrete shall be in accordance with Section 3107F.2.4.1.

Each structural component expected to undergo inelas- tic deformation shall be defined by its moment-curvature

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FIGURE 31F-7-3 STRESS-STRAIN CURVE FOR PRESTRESSED STEEL [7.4]

3107F.2.5 Concrete piles.

3107F.2.5.1 General. The capacity of concrete piles is based on permissible concrete and steel strains corre- sponding to the desired performance criteria.

Different values may apply for plastic hinges form- ing at in-ground and pile-top locations. These proce- dures are applicable to circular, octagonal, rectangular and square pile cross sections.

3107F.2.5.2 Stability. Stability considerations are important to pier-type structures. The moment-axial load interaction shall consider effects of high slender- ness ratios (kl/r). An additional bending moment due to axial load eccentricity shall be incorporated unless:

e/h ≤ 0.10 (7-4)

where:

e = eccentricity of axial load

h = width of pile in considered direction

3107F.2.5.3 Plastic hinge length. The plastic hinge length is required to convert the moment-curvature relationship into a moment-plastic rotation relation- ship for the nonlinear pushover analysis.

The pile’s plastic hinge length, Lp (above ground) for reinforced concrete piles, when the plastic hinge forms against a supporting member is:

Lp = 0.08 L + 0.15 fye db ≥ 0.3 fye db (7-5)

where:

L = distance from the critical section of the plastic

hinge to the point of contraflexure

db = diameter of the longitudinal reinforcement or

dowel, whichever is used to develop the connection

fye = design yield strength of longitudinal reinforcement or dowel, whichever is used to develop the connection (ksi)

CONNECTION TYPE	L AT DECK (in.) p
Pile Buildup	0.15fyedb ≤ Lp ≤ 0.30fyedb
Extended Strand	0.20fpyedst
Embedded Pile	0.5D
Dowelled	0.25fyedb
Hollow Dowelled	0.20fyedb
External Confinement	0.30fyedb
Isolated Interface	0.25fyedb

cu = neutral-axis depth, at ultimate strength of

section

If a large reduction in moment capacity occurs due to spalling, then the plastic hinge length shall be:

Lp = 0.3 fye db (7-6)

The plastic hinge length, Lp (above ground), for pre- stressed concrete piles may also be computed from Table 31F-7-4 for permitted pile-to-deck connections as described in ASCE/COPRI 61 [7.5].

When the plastic hinge forms in-ground, the plastic hinge length may be determined using Equation (7-7)

[7.5]:

Lp = 2D (7-7)

where:

D = pile diameter or least cross-sectional dimension

TABLE 31F-7-4 PLASTIC HINGE LENGTH FOR PRESTRESSED CONCRETE PILES [7.5]

db = diameter of the prestressing strand or dowel, whichever is used to

develop the connection (in.) fye = design yield strength of prestressing strand or dowel, as appropriate

(ksi) D = pile diameter or least cross-sectional dimension dst = diameter of the prestressing strand (in.) fpye = design yield strength of prestressing strand (ksi)

3107F.2.5.4 Plastic rotation. The plastic rotation is:

θ p = Lp φ p = Lp ( φ m - φ y) (7-8)

where:

Lp = plastic hinge length

φ p = plastic curvature

φ m = maximum curvature

φ y = yield curvature

The maximum curvature, φ m shall be determined by the concrete or steel strain limit state at the prescribed performance level, whichever comes first.

Alternatively, the maximum curvature, φ m may be calculated as:

ε cm φ m = ----- -

where:

(7-9)

ε cm = maximum limiting compression strain for the

prescribed performance level (Table 31F-7-5)

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TABLE 31F-7-5 LIMITS OF STRAIN

COMPONENT STRAIN	LEVEL 1	LEVEL 2
MCCS Pile/deck hinge	ε_c_ ≤ 0.004	ε_c_ ≤ 0.025
MCCS In-ground hinge	ε_c_ ≤ 0.004	ε_c_ ≤ 0.008
MRSTS Pile/deck hinge	ε_s_ ≤ 0.01	ε_s_ ≤ 0.05
MRSTS In-ground hinge	ε_s_ ≤ 0.01	ε_s_ ≤ 0.025
MPSTS In-ground hinge	ε_p_ ≤ 0.005 (incremental)	ε_p_ ≤ 0.025 (total strain)

MCCS = Maximum Concrete Compression Strain, ε c MRSTS = Maximum Reinforcing Steel Tension Strain, ε s MPSTS = Maximum Prestressing Steel Tension Strain, ε p

Either Method A or B may be used for idealization of the moment-curvature curve.

3107F.2.5.4.1 Method A. For Method A, the yield curvature, φ y is the curvature at the intersection of the secant stiffness, EIc, through first yield and the nominal strength, ( ε c = 0.004).

My φ y = ------EIc

METHOD A - MOMENT CURVATURE ANALYSIS

(7-10)

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FIGURE 31F-7-5 METHOD B – MOMENT CURVATURE ANALYSIS [7.6]

3107F.2.5.5 Ultimate concrete and steel flexural strains. Strain values computed in the nonlinear push- over analysis shall be compared to the following lim- its.

3107F.2.5.5.1 Unconfined concrete piles: An unconfined concrete pile is defined as a pile having no confinement steel or one in which the spacing of the confinement steel exceeds 12 inches.

Ultimate concrete compressive strain:

ε cu = 0.005 (7-11)

3107F.2.5.5.2 Confined concrete piles: Ultimate concrete compressive strain [7.1]:

ε cu = 0.004 + (1.4 ρ s fyh ε sm)/f ′ cc ≥ 0.005 (7-12)

ε cu ≤ 0.025

where:

ρ s = effective volume ratio of confining steel

fyh = yield stress of confining steel

ε sm = strain at peak stress of confining reinforcement, 0.15 for grade 40, 0.10 for grade 60

f ′ cc = confined strength of concrete approximated

by 1.5 f ′ c 3107F.2.5.6 Component acceptance/damage criteria. The maximum allowable concrete strains may not exceed the ultimate values defined in Section 3107F.2.5.5. The limiting values (Table 31F-7-5) apply for each perfor- mance level for both existing and new structures. The “Level 1 or 2” refer to the seismic performance criteria (see Section 3104F.2.1).

For all non-seismic loading combinations, concrete components shall be designed in accordance with the ACI 318 [7.7] requirements.

Note that for existing facilities, the pile/deck hinge may be controlled by the capacity of the dowel rein- forcement in accordance with Section 3107F.2.7.

3107F.2.5.4.2 Method B. For Method B, the elas- tic portion of the idealized moment-curvature curve is the same as in Method A (see Section 3107F.2.5.4.1). However, the idealized plastic moment capacity, Mp, and the yield curvature, φ y, is obtained by balancing the areas between the actual and the idealized moment-curvature curves beyond the first yield point (see Figure 31F-7-5). Method B applies to moment-curvature curves that do not experience reduction in section moment capacity.

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3107F.2.5.7 Shear design. If expected lower bound of material strength Section 3107F.2.1.1 Equations (7-2a, 7-2b, 7-2c) are used in obtaining the nominal shear strength, a new nonlinear analysis utilizing the upper bound estimate of material strength Section 3107F.2.1.1 Equations (7-3a, 7-3b, 7-3c) shall be used to obtain the plastic hinge shear demand. An alterna- tive conservative approach is to multiply the maximum shear demand, Vmax from the original analysis by 1.4 (Section 8.16.4.4.2 of ATC-32 [7.8]):

Vdesign = 1.4Vmax (7-13)

If moment curvature analysis that takes into account strain-hardening, an uncertainty factor of 1.25 may be used:

Vdesign = 1.25Vmax (7-14)

Shear capacity shall be based on nominal material strengths, and reduction factors according to ACI 318

[7.7].

As an alternative, the method of Kowalski and Priestley [7.9] may be used. Their method is based on a three-parameter model with separate contributions to shear strength from concrete (Vc), transverse reinforce- ment (Vs), and axial load (Vp) to obtain nominal shear strength (Vn):

Vn = Vc + Vs + Vp (7-15)

A shear strength reduction factor of 0.85 shall be applied to the nominal strength, Vn, to determine the design shear strength. Therefore:

Vdesign ≤ 0.85Vn (7-16)

The equations to determine Vc, Vs and Vp are:

where:

(7-17)

k = factor dependent on the curvature ductility μφ =

φ ---- φ y

, within the plastic hinge region, from

Figure 31F-7-6. For regions greater than 2Dp (see Equation 7-18) from the plastic hinge location, the strength can be based on mf = 1.0 (see Ferritto et. al. [7.2]).

f ′ c = concrete compressive strength

Ae = 0.8Ag is the effective shear area

Circular spirals or hoops [7.2]:

Vs = ------------------------------------------------------------------π ^- 2 ^- Asp ^f yh ( ^D p - c - co ) cot (θ) s

where:

Asp= spiral or hoop cross section area

(7-18)

fyh = yield strength of transverse or hoop reinforcement

Dp= pile diameter or gross depth (in case of a

rectangular pile with spiral confinement)

c = depth from extreme compression fiber to

neutral axis (N.A.) at flexural strength (see Figure 31F-7-7)

c0 = distance from concrete cover to center of hoop

or spiral (see Figure 31F-7-7)

FIGURE 31F-7-6 CONCRETE SHEAR MECHANISM

(from Fig. 3-30 of [7.2])

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θ =angle of critical crack to the pile axis (see

Figure 31F-7-7) taken as 30° for existing structures, and 35° for new design

s = spacing of hoops or spiral along the pile axis

FIGURE 31F-7-7 TRANSVERSE SHEAR MECHANISM

Rectangular hoops or spirals [7.2]:

Ah fyh ( Dp - c - co ) cot (θ) Vs = ------------------------------------------------------------s

where:

(7-19)

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FIGURE 31F-7-8 AXIAL FORCE SHEAR MECHANISM

3107F.2.6.3 Plastic hinge length. The plastic hinge length, Lp (above ground), for steel piles may be com- puted from Table 31F-7-6 for pile-to-deck connections.

When the plastic hinge forms in-ground, the plastic hinge length may be determined using Equation (7-21)

[7.5]:

Lp = 2D (7-21)

where:

D = pile diameter

TABLE 31F-7-6 PLASTIC HINGE LENGTH FOR STEEL PILES [7.5]

CONNECTION TYPE	L AT DECK (in.) p
Embedded Pile	0.5D
Concrete Plug	0.30fyedb
Isolated Shell	0.30fyedb+g
Welded Embed	0.5D

db = diameter of the dowel (in.) fye = design yield strength of dowel (ksi) D = pile diameter (in.) g = gap distance from bottom of the deck to edge of pipe pile or external

confinement (in.)

3107F.2.6.4 Ultimate flexural strain capacity. The fol- lowing limiting value applies:

Strain at extreme-fiber, ε u ≤ 0.035

3107F.2.6.5 Component acceptance/damage criteria. The maximum allowable strain may not exceed the ulti- mate value defined in Section 3107F.2.6.4. Table 31F- 7-7 provides limiting strain values for each perfor- mance level, for both new and existing structures.

Ah = total area of transverse reinforcement, parallel to direction of applied shear cut by an inclined shear crack

Shear strength from axial mechanism, Vp (see Figure 31F-7-8):

Vp = Φ ( Nu + Fp ) tan α (7-20)

where:

Nu = external axial compression on pile including

seismic load. Compression is taken as positive; tension as negative

Fp = prestress compressive force in pile

α =angle between line joining centers of flexural

compression in the deck/pile and in-ground hinges, and the pile axis

Φ =1.0 for existing structures, and 0.85 for new

design

3107F.2.6 Steel piles.

3107F.2.6.1 General. The capacity of steel piles is based on allowable strains corresponding to the desired performance criteria and design earthquake.

3107F.2.6.2 Stability. Section 3107F.2.5.2 applies to steel piles.

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Steel components for noncompact hollow piles (DP / t < 0.07 × E/fy) and for all nonseismic loading combi- nations shall be designed in accordance with AISC 325

[7.10].

TABLE 31F-7-7 STRUCTURAL STEEL STRAIN LIMITS, ε u

Level 1 or 2 refer to the seismic performance criteria (Section 3104F.2.1)

3107F.2.6.6 Shear design. The procedures of Section 3107F.2.5.7, which are used to establish Vdesign are applicable to steel piles.

The shear capacity shall be established from the AISC 325 [7.10]. For concrete filled pipe, Equation (7- 15) may be used to determine shear capacity; however, Vpile must be substituted for Vs.

Vpile = (π/2) tfy, pile ( Dp - c - co ) cot θ (7-22)

where:

t = steel pile wall thickness

fy,pile = yield strength of steel pile

c0 = distance from outside of steel pipe to center of

hoop or spiral

[All other terms are as listed for Equation (7-18)].

3107F.2.7 Pile/deck connection strength.

3107F.2.7.1 Joint shear capacity. The joint shear capacity shall be computed in accordance with ACI 318 [7.7]. For existing MOTs, the method [7.1, 7.2] given below may be used:

1. Determine the nominal shear stress in the joint region corresponding to the pile plastic moment capacity.

2. Determine the nominal principal tension pt, stress in the joint region:

(7-24)

(7-25)

fa pt = -----

where:

N fa = ----------------------( Dp + hd ) - 2

0.9 Mo

where:

vj = Nominal shear stress

(7-23)

is the average compressive stress at the joint cen- ter caused by the pile axial compressive force N and hd is the deck depth. Note, if the pile is sub- jected to axial tension under seismic load, the value of N, and fa will be negative.

a lower moment than the column plastic moment capacity Mp. In this case, the maximum moment that can be developed at the pile/deck interface will be limited by the joint principal tension stress capacity, which will continue to degrade as the joint rotation increases, as shown in Figure 31F-7-10. The moment capacity of the connec- tion at which joint failure initiates can be estab- lished from Equations (7-27) and (7-28).

FIGURE 31F-7-10 DEGRADATION OF EFFECTIVE PRINCIPAL TENSION STRENGTH WITH JOINT

SHEAR STRAIN (rotation) [7.1, pg. 564]

ing joint shear stress, vj:

Mo = Overstrength moment demand of the

plastic hinge (the maximum possible moment in the pile) as determined from the procedure of Section 3107F.2.5.7.

(7-26)

ldv = Vertical development length, see Figure

31F-7-9

Dp = Diameter of pile

FIGURE 31F-7-9 DEVELOPMENT LENGTH

This will result in a reduced strength and effec- tive stiffness for the pile in a pushover analysis. The maximum displacement capacity of the pile should be based on a drift angle of 0.04 radians.

If no mechanisms are available to provide residual strength, the moment capacity will decrease to zero as the joint shear strain

3. The moment capacity of the connection can be approximated as:

0.9

(7-27)

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increases to 0.04 radians, as shown in Figure 31F-7-11.

FIGURE 31F-7-11 REDUCED PILE MOMENT CAPACITY

If deck stirrups are present within hd/2 of the face of the pile, the moment capacity, Mc,r, at the maximum plastic rotation of 0.04 radians may be increased from zero to the following (see Figure 31F-7-12):

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4. Using the same initial stiffness as in Section 3107F.2.5.4, the moment-curvature relationship established for the pile top can now be adjusted to account for the joint degradation.

The adjusted yield curvature, φ′ y, can be found from:

(7-32)

φ yMc φ′ y = ---------- Mp

where:

(7-30)

Mp = Idealized plastic moment capacity from

Method A or B (see Figure 31F-7-4 or 31F-7-5, respectively)

The plastic curvature, φ p, corresponding to a joint rotation of 0.04 can be calculated as:

0.04 φ p = -------- - Lp

where:

(7-31)

Lp = Plastic hinge length as determined from

Equation (7-5)

The adjusted ultimate curvature, φ ′ u, can now be calculated as:

Mc, r = 2 As fy ( hd - dc ) + N ^Dp - dc

^---- 2 ^-

where:

(7-28)

φ yMc, r φ′ u = φ p + -------------Mp

where:

As = Area of slab stirrups on one side of joint

hd = See Figure 31F-7-9 (deck thickness)

dc = Depth from edge of concrete to center of

main reinforcement

In addition, the bottom deck steel (As, deckbottom) area within hd/2 of the face of the pile shall sat- isfy:

As, deckbottom ≥ 0.5 · As (7-29)

Mp = Idealized plastic moment capacity from

Method A or B (see Figure 31F-7-4 or 31F-7-5, respectively)

Mc,r = 0, unless deck stirrups are present as

discussed above.

Examples of adjusted moment curvature rela- tionships are shown in Figure 31F-7-13 .

FIGURE 31F-7-13 FIGURE 31F-7-12 EQUIVALENT PILE CURVATURE JOINT ROTATION

MARINE OIL TERMINALS

3107F.2.7.2 Development length. The minimum devel- opment length, ldc, is:

0.025 ⋅ db ⋅ fye

where:

db = dowel bar diameter

fye = expected yield strength of dowel

f ′ c= compressive strength of concrete

(7-33)

In assessing existing details, actual or estimated values for fye and f'c rather than nominal strength should be used in accordance with Section 3107F.2.1.1.

When the development length is less than that cal- culated by the Equation ( 7-33), the moment capacity shall be calculated using a proportionately reduced yield strength, fye,r, for the vertical pile reinforce- ment:

ld fye, r = fye ⋅ --- - ldc

where :

ld = actual development length

fye = expected yield strength of dowel

3107F.2.8 Batter piles.

(7-34)

shown in Figure 31F-7-14 for a wharf supported by one row of batter piles.

FIGURE 31F-7-14 PUSHOVER CURVE FOR ORDINARY BATTER PILES

When the row of batter piles fail in tension or shear, stored energy will be released. The structure will there- fore experience a lateral displacement demand follow- ing the nonductile pile failures. If the structure can respond to this displacement demand without exceed- ing other structural limitations, it may be assumed that the structure is stable and will start to respond to fur- ther shaking with a much longer period and corre- sponding lower seismic demands. The wharf structure may therefore be able to sustain larger seismic demands following the loss of the batter piles than before the loss of pile capacity, because of a much softer seismic response.

The area under the pushover curve before the batter pile failures is compared to the equivalent area under the post failure pushover curve (refer to Figure 31F-7- 14). If no other structural limitations are reached with the new displacement demand, it is assumed that the structure is capable of absorbing the energy. It should be noted that even though the shear failure is nonduc- tile, it is expected that energy will be absorbed and the damping will increase during the damage of the piles. The above method is, therefore, considered conserva- tive.

Following the shear failure of a batter pile row, the period of the structure increases such that equal dis- placement can be assumed when estimating the post- failure displacement demand. The new period may be estimated from the initial stiffness of the post-failure system as shown in Figure 31F-7-14. A new displace- ment demand can then be calculated in accordance with Section 3104F.2.

3107F.2.8.1 Existing ordinary batter piles. Wharves or piers with ordinary (not fused, plugged or having a seismic release mechanism) batter piles typically have a very stiff response when subjected to lateral loads in the direction of the batter. The structure often main- tains most of its initial stiffness all the way to failure of the first row of batter piles. Since batter piles most likely will fail under a Level 2 seismic event, the follow- ing method may be used to evaluate the post-failure behavior of the wharf or pier:

1. Identify the failure mechanism of the batter pile- deck connection (refer to Section 3104F.4.7) for typical failure scenarios) and the corresponding lateral displacement.

2. Release the lateral load between the batter pile and the deck when the lateral failure displace- ment is reached.

3. Push on the structure until subsequent failure(s) have been identified.

As an example, following these steps will result in a force-displacement (pushover) curve similar to the one

31F-64 2022 CALIFORNIA BUILDING CODE

3107F.2.8.2 Nonordinary batter piles. For the case of a plugged batter pile system, an appropriate displace- ment force relationship considering plug friction may be used in modeling the structural system.

For fused and seismic release mechanism batter pile systems, a nonlinear modeling procedure shall be used and peer reviewed (Section 3101F.8.2). 3107F.2.9 Concrete pile caps with concrete deck. Pile caps and decks are capacity protected components. Use the procedure of Section 3107F.2.5.7 to establish the over strength demand of the plastic hinges. Component capac- ity shall be based on nominal material strengths, and reduction factors according to ACI 318 [7.7].

3107F.2.9.1 Component acceptance/damage criteria. For new pile caps and deck, Level 1 seismic perfor- mance shall utilize the design methods in ACI 318 [7.7]; Level 2 seismic performance shall be limited to the fol- lowing strains:

Deck/pile cap: ε c ≤ 0.005

Reinforcing steel tension strain: ε S ≤ 0.01

For existing pile caps and deck, the limiting strain values are defined in Table 31F-7-5.

Concrete components for all nonseismic loading combinations shall be designed in accordance with ACI 318 [7.7].

3107F.2.9.2 Shear capacity (strength). Shear capacity shall be based on nominal material strengths; reduc- tion factors shall be in accordance with ACI 318 [7.7]. 3107F.2.10 Concrete detailing. For new MOTs, the required development splice length, cover and detailing shall conform to ACI 318 [7.7], with the following excep- tions:

1. For pile/deck dowels, the development length may be calculated in accordance with Section 3107F.2.7.2.

2. The minimum concrete cover for prestressed con- crete piles shall be three inches, unless corrosion inhibitors are used, in which case a cover of two- and-one-half inches is acceptable.

3. The minimum concrete cover for wharf beams and slabs, and all concrete placed against soil shall be three inches, except for headed reinforcing bars (pile dowels or shear stirrups) the cover may be reduced to two-and-one-half inch cover at the top surface only. If corrosion inhibitors are used, a cover of two-and-one-half inches is acceptable.

3107F.3 Timber piles and deck components.¶

3107F.3.1 Component strength. The following parame- ters shall be established in order to assess component strength:

New and existing components:

1. Modulus of rupture

2. Modulus of elasticity

3. Type and grade of timber

MARINE OIL TERMINALS

Existing components only:

1. Original cross-section shape and physical dimen- sions

2. Location and dimension of braced frames

3. Current physical condition of members including visible deformation

4. Degradation may include environmental effects (e.g., decay, splitting, fire damage, biological and chemical attack) including its effect on the moment of inertia, I

5. Loading and displacement effects (e.g., overload, damage from earthquakes, crushing and twist- ing) Section 3104F.2.2 discusses existing material proper- ties. At a minimum, the type and grade of wood shall be established. The adjusted reference design values per Sec- tion 6 of ANSI/AWC NDS [7.11] may be used.

For deck components, the adjusted design stresses shall be limited to the values of ANSI/AWC NDS [7.11]. Piling deformation limits shall be calculated based on the strain limits in accordance with Section 3107F.3.3.3.

The values shown in the ANSI/AWC NDS [7.11] are not developed specifically for MOTs and can be used as default properties only if as-built information is not available, the member is not damaged and testing is not performed. To account for the inherent uncertainty in establishing component capacities for existing structures with limited knowledge about the actual material proper- ties, a reduction (knowledge) factor of k = 0.75 shall be included in the component strength and deformation capacity analyses in accordance with Section 3107F.2.1.2.

The modulus of elasticity shall be based on tests or Sec- tion 4 for deck components and Section 6 for timber piles of ANSI/AWC NDS [7.11].

3107F.3.2 Deformation capacity of flexural members. The displacement demand and capacity of existing timber structures may be established per Section 3104F.2.

The soil spring requirements for the lateral pile analy- sis shall be in accordance with Section 3106F.

A linear curvature distribution may be assumed along the full length of a timber pile.

The displacement capacity of a timber pile can then be established per Section 3107F.3.3.2.

3107F.3.3 Timber piles.

3107F.3.3.1 Stability. Section 3107F.2.5.2 shall apply to timber piles.

3107F.3.3.2 Displacement capacity. A distinction shall be made between a pier-type pile, with a long unsup- ported length and a wharf-landside-type pile with a short unsupported length between the deck and soil. The effective length, L, is the distance between the pinned deck/pile connection and in-ground fixity as shown in Figure 31F-7-15. For pier-type (long unsup- ported length) vertical piles, three simplified proce-

stinction shall_ be made between a pier-type pile, with a long unsup- ported length and a wharf-landside-type pile with a short unsupported length between the deck and soil. The effective length, L, is the distance between the pinned deck/pile connection and in-ground fixity as shown in Figure 31F-7-15. For pier-type (long unsup- ported length) vertical piles, three simplified proce-

MARINE OIL TERMINALS

dures to determine fixity or displacement capacity are described in UFC 4-151-10 [7.12], UFC 3-220-01

[7.13] and Chai [7.14].

In order to determine fixity in soft soils, another alternative is to use Table 31F-7-8.

The displacement capacity, Δ , for a pile pinned at the top, with effective length, L, (see Table 31F-7-8 and UFC 4-151-10 [7.12]), and moment, M, is:

(7-35)

ML 2 Δ = -------- -

3107F.3.3.3 Component acceptance/damage criteria. The following limiting strain values apply for each seis- mic performance level for existing structures:

TABLE 31F-7-9 LIMITING STRAIN VALUES FOR TIMBER

EARTHQUAKE LEVEL	MAX. TIMBER STRAIN
Level 1	0.002
Level 2	0.004

For new and alternatively, for existing structures ANSI/AWC NDS [7.11] may be used.

Timber components for all non-seismic loading combinations shall be designed in accordance with ANSI/AWC NDS [7.11].

3107F.3.3.4 Shear design. To account for material strength uncertainties, the maximum shear demand, Vmax, established from the single pile lateral analysis shall be multiplied by 1.2:

Vdemand = 1.2 Vmax (7-40)

The factored maximum shear stress demand τ max, in a circular pile can then be determined:

= -------- - 3 EI

where:

E = Modulus of elasticity

I = Moment of inertia

FIGURE 31F-7-15 ASSUMED IN-GROUND FIXITY

TABLE 31F-7-8 DISTANCE BELOW GROUND TO POINT OF FIXITY

PILE EI g	SOFT CLAYS	LOOSE GRANULAR & MEDIUM CLAYS
< 1010 lb in2	10 feet	8 feet
> 1010 lb in2	12 feet	10 feet

Assuming linear curvature distribution along the pile, the allowable curvature, φ a, can be established from:

10 τ max = -------------- ^---- 9 ^- ^V π ^demand ⋅ r ²

where:

r = radius of pile

(7-41)

ε a φ a = ^-- c ^-

where:

(7-36)

ε a = allowable strain limit according to Section 3107F.3.3.3

c = distance to neutral axis which can be taken as

Dp/2, where Dp is the diameter of the pile

The curvature is defined as:

M φ = ---- - EI

(7-37)

The maximum allowable moment therefore becomes:

2ε a M = ------- EI Dp

(7-38)

For the seismic load combinations, the maximum allowable shear stress, τ capacity, is the design shear strength, τ design, from the ANSI/AWC NDS [7.11] multi- plied by a factor of 2.8.

τ capacity = 2.8τ design (7-42)

The shear capacity must be greater than the maxi- mum demand.

3107F.4 Retaining structures.¶

Retaining structures con- structed of steel or concrete shall conform to AISC 325 [7.10] or ACI 318 [7.7], respectively. For the determination of static and seismic loads on the sheet pile and sheet pile behavior, the following references are acceptable: Ebeling and Morri- son [7.15], Strom and Ebeling [7.16], and PIANC TC-7 (Technical Commentary - 7) [7.17]. The applied loads and analysis methodology shall be determined by a California registered geotechnical engineer, and may be subject to peer review.

3107F.5 Nonbuilding structures and building structures.¶

The analysis of nonbuilding structures and building struc- tures shall be based on the load combinations defined in Sec- tion 3103F.8 with seismic assessment per Section 3104F.5. The component strength in nonbuilding structures and build- ing structures shall be established in accordance with AISC

[7.10], ACI-318 [7.7] and ANSI/AWC NDS [7.11], account- ing for existing condition with knowledge factors applied, as appropriate. For strength evaluation of supports and attach- ments, see Section 3107F.7.

The displacement capacity is therefore given by:

2ε aL 2 Δ = ----------- -

3 Dp

(7-39)

31F-66 2022 CALIFORNIA BUILDING CODE

3107F.6 Mooring and berthing components.¶

Mooring com- ponents include bitts, bollards, cleats, pelican hooks, cap- stans, mooring dolphins and quick release hooks. The maximum mooring line forces (demand) shall be established per Section 3105F. Applicable safety factors to be applied to the demand are provided in Section 3105F.8. Multiple lines may be attached to the mooring component at varying hori- zontal and vertical angles. Mooring components shall there- fore be checked for all mooring analysis load cases.

Berthing components include fender piles and fenders, which may be camels, fender panels or wales. The maximum berthing forces (demand) on breasting dolphins and fender piles shall be established according to Section 3105F.

Mooring and berthing components analyses shall be based on the load combinations defined in Section 3103F.8 with seismic assessment per Section 3104F.5. The component strength shall account for existing condition with knowledge factors applied, as appropriate. For strength evaluation of supports and attachments, see Section 3107F.7.

Mooring and berthing component capacities may be gov- erned by the strength of the deck, structure and/or soil. Therefore, a check of the deck, structural and geotechnical capacities to withstand component loads shall be performed, as appropriate.

3107F.7 Supports and attachments (or anchorage).¶

The evaluation of supports and attachments for nonstructural components, nonbuilding structures and building structures shall be based on the load combinations defined in Section 3103F.8 with seismic assessment per Section 3104F.5. The strength of supports and attachments for nonstructural com- ponents, nonbuilding structures and building structures shall be assessed in accordance with AISC [7.10], ACI-318 [7.7] and ANSI/AWC NDS [7.11], accounting for existing condi- tion with knowledge factors applied, as appropriate. The fol- lowing parameters shall be established to calculate strength:

New and existing components:

1. Yield and tensile strength of structural steel 2. Structural steel modulus of elasticity

3. Yield and tensile strength of bolts

4. Concrete infill compressive strength

5. Concrete infill modulus of elasticity

Additional parameters for existing components:

1. Condition of steel including corrosion

2. Effective cross-sectional areas 3. Condition of embedment material such as concrete slab or timber deck

The analysis and design shall include the load transfer to supporting deck/pile structures or foundation elements. A check of the deck capacity to withstand support and attach- ment loads shall be performed for all nonstructural compo- nents, nonbuilding structures and building structures.

3107F.8 Symbols.¶

Ae = Effective shear area

Ag = Uncracked, gross section area

MARINE OIL TERMINALS

Ah = Total area of transverse reinforcement, parallel

to direction of applied shear cut by an inclined shear crack

As = Area of slab stirrups on one side of joint

As, deckbottom=Area of bottom deck steel

Asp = Spiral or hoop cross section area

c = Depth from extreme compression fiber to neutral

axis at flexural strength

c0 = Distance from outside of steel pipe to center of

hoop or spiral, or distance from concrete cover to center of hoop or spiral

cu = Neutral axis depth at ultimate strength of section

db = Diameter of the longitudinal reinforcement,

prestressing strand or dowel, as appropriate

dc = Depth from edge of concrete to center of main

reinforcement

dst = Diameter of the prestressing strand (in)

D = Pile diameter or least cross-sectional dimension

Dp = Pile diameter or gross depth (in case of a

rectangular pile with spiral confinement)

e = Eccentricity of axial load

ε a = Allowable strain limit

ε c = Concrete compressive strain

ε cm = Maximum extreme fiber compression strain

ε cu = Ultimate concrete compressive strain

ε p = Prestressing steel tension strain

ε s = Reinforcing steel tension strain ε sm = Strain at peak stress of confining reinforcement

ε u = Ultimate steel strain

E = Modulus of elasticity

Ec = Modulus of elasticity for concrete

Es = Modulus of elasticity for steel

f ′ c = Concrete compression strength f ′ cc = Confined strength of concrete

Fp = Prestress compression force in pile

fp = Yield strength of prestressing strand

fpye = Design yield strength of prestressing strand (ksi)

fy = Yield strength of steel

fye = Design yield strength of longitudinal reinforcement,

prestressing strand or dowel, as appropriate (ksi)

fyh = Yield stress of confining steel

fyh = Yield strength of transverse or hoop reinforcement

fy,pile = Yield strength of steel pile

fye,r = Reduced dowel yield strength

g = Gap distance from bottom of the deck to edge of

pipe pile or external confinement (in.)

h = Width of pile in considered direction

MARINE OIL TERMINALS

hd = Deck depth

I = Moment of inertia

Ic = Moment of inertia of uncracked section

Ie = Effective moment of inertia

Ig = Gross moment of inertia

Is = Moment of inertia for steel section

k = Factor dependent on the curvature ductility μφ =

φ / φ y, within the plastic hinge region

k = Knowledge factor

L = Distance from the critical section of the

plastic hinge to the point of contraflexure (Section 3107F.2.5.3), or effective length (Section 3107F.3.3.2)

Lp = Plastic hinge length

ldc = Minimum development length

ld = Actual development length

ldv = Vertical development length

M = Maximum allowable moment

Mc = Moment capacity of the connection

Mc,r = Moment capacity at maximum plastic rotation

Mo = Overstrength moment demand of the plastic hinge

(Section 3107F.2.7)

Mp = Idealized plastic moment capacity from Method A

or B (Section 3107F.2.5)

My = Moment at first yield

N = Pile axial compressive force

Nu = External axial compression on pile including

seismic load

ρ s = Effective volume ratio of confining steel

pt = Nominal principal tension

r = Radius of circular pile

s = Spacing of hoops or spiral along the pile axis t = Steel pile wall thickness

Δ = Displacement capacity

θ = Angle of critical crack to the pile axis

θ p = Plastic rotation

α = Angle between line joining centers of flexural

compression in the deck/pile and in-ground hinges, and the pile axis

φ a = Allowable curvature

φ m = Maximum curvature

φ p, φ p,m = Plastic curvature

φ u = Ultimate curvature

φ ′ u = Adjusted ultimate curvature

φ y = Yield curvature

φ ′ y = Adjusted yield curvature

τ capacity = Maximum allowable shear stress

τ design = Design shear strength

τ max = Maximum shear stress

Vc = Concrete shear strength

vj = Nominal joint shear stress

Vdesign= Design shear strength

Vmax = Maximum shear demand

Vn = Nominal shear strength

Vp = Contribution to shear strength from axial loads

Vs = Transverse reinforcement shear strength

Vpile = Shear strength of steel pile

3107F.9 References.¶

[7.1] Priestley, M.J.N, Seible, F. and Calvi, G.M. “Seis-

mic Design and Retrofit of Bridges,” 1996, New York.

[7.2] Ferritto, J., Dickenson, S., Priestley N., Werner, S.,

Taylor, C., Burke D., Seelig W., and Kelly, S., 1999, “Seismic Criteria for California Marine Oil Termi- nals, Vol.1 and Vol.2,” Technical Report TR-2103- SHR, Naval Facilities Engineering Service Center, Port Hueneme, CA.

[7.3] American Society of Civil Engineers (ASCE), 2017,

ASCE/SEI 41-17 (ASCE/SEI 41), “Seismic Evalua- tion and Retrofit of Existing Buildings,” Reston, VA.

[7.4] Blakeley, J.P., Park, R., “Prestressed Concrete Sec-

tions with Cyclic Flexure,” Journal of the Structural Division, American Society of Civil Engineers, Vol. 99, No. ST8, August1973, pp. 1 71 7-1 742, Reston, VA.

[7.5] American Society of Civil Engineers (ASCE), 2014,

ASCE/COPRI 61-14 (ASCE/COPRI 61), “Seismic Design of Piers and Wharves,” Reston, VA.

[7.6] Port of Long Beach (POLB), 2012 February 29,

“Wharf Design Criteria,” Version 3.0, Long Beach, CA.

[7.7] American Concrete Institute (ACI), 2014, ACI 318-

14 (ACI 318), “Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary (ACI 318R-14),” Farmington Hills, MI.

[7.8] Applied Technology Council (ATC), 1996, ATC-32,

“Improved Seismic Design Criteria for California Bridges: Provisional Recommendations,” Redwood City, CA.

[7.9] Kowalski, M.J. and Priestley, M.J.N., June 1998,

“Shear Strength of Ductile Bridge Columns,” Proc. 5th Caltrans Seismic Design Workshop, Sacra- mento, CA.

[7.10] American Institute of Steel Construction Inc.

(AISC), 2017, AISC 325-17 (AISC 325), “Steel Con- struction Manual,” 15th ed., Chicago, IL.

31F-68 2022 CALIFORNIA BUILDING CODE

MARINE OIL TERMINALS

[7.11] American Wood Council (AWC), 2017, ANSI/AWC

NDS-2018 (ANSI/AWC NDS) “National Design Specification (NDS) for Wood Construction,” Wash- ington, D.C.

[7.12] Department of Defense, 10 September 2001

(Revised 1 September 2012), Unified Facilities Cri- teria (UFC) 4-151-10, “General Criteria for Water- front Construction,” Washington, D.C.

[7.13] Department of Defense, 01 November 2012, Unified

Facilities Criteria (UFC) 3-220-01, “Geotechnical Engineering,” Washington, D.C.

[7.14] Chai, Y.H., “Flexural Strength and Ductility of

Extended Pile-Shafts, I: Analytical Model,” Journal of Structural Engineering, May 2002, pp. 586–594.

[7.15] Ebeling, Robert M. and Morrison, Ernest E., Jr.,

November 1992, “The Seismic Design of Waterfront Retaining Structures”, U.S. Army Technical Report ITL-92-11/U.S. Navy Technical Report NCEL TR 939, Dept. of Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, MS.

[7.16] Strom, Ralph W. and Robert M. Ebeling, December

2001,“State of the Practice in the Design of Tall, Stiff, and Flexible Tieback Retaining Walls,” Infor- mation Technology Laboratory, Engineer Research and Development Center, U.S. Army Corps of Engi- neers, Vicksburg, MS.

[7.17] Permanent International Association of Navigation

Congresses (PIANC), “Seismic Design Guidelines for Port Structures,” Technical Commentary-7, Working Group No. 34 of the Maritime Navigation Commission International Navigation Association, A.A. Balkema, Lisse, Netherlands. 2001. Authority: Sections 8750 through 8760, Public Resources Code.

Reference: Sections 8750, 8751, 8755 and 8757, Public Resources Code.

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Division 8